Master Thesis

P-release kinetic as a predictor for P-availability in the STYCS Trials

Marc Jerónimo Pérez y Ropero

Introduction

  • In my Internship I studied the current GRUD, particularly Mg, P and K

  • Fertilizer requirement models imply \(Y\sim STP + Clay\) & \(P-\text{Export}\sim STP + Clay\)

  • Currently only stationary measurement of STP are considered

  • Could a kinetic desorption-model better explain the soil status and yield data?

The STYCS Experiment

  • LTE STYCS, all treatment conditions equal except P-fertilization, which is in 6 Levels, 3 were considered(\(P0\),\(P100\),\(P166\))
  • 4 Sites regarded; Ellighausen, Rümlang-Altwi, Oensingen, Zürich-Reckenholz
  • 5 Sites, 4 blocks per site, 6 Treatment-Levels, 4 Repetitions
  • Years 2017-2022 were modelled, kinetic data was collected only for year 2022

A kinetic Approach to P

The net-desorption was modeled using a first-order kinetic equation:

1. The Rate of Release: The change in P over time is proportional to the remaining desorbable P. \[\frac{dP}{dt}=k \times (P^S-P)\]

2. The Solution: When solved, this gives us the equation for the curve: \[P(t)=P^S \times (1-e^{-kt})\]

  • \(P^S\) (PS): The maximum desorbable P pool.
  • \(k\): The first-order rate constant.

Adapted Kinetic-Experiment Setup

Method Validation

Method Validation

Method Validation

Method Validation

The Competing Predictors

We compared two approaches to predict agronomic outcomes:

The Standard Method

  • \(P_{CO2}\)
  • \(P_{AAE10}\)

These are static “snapshots” of the soil’s P capacity.

The Kinetic Method

  • PS (\(P^S\)): The size of the available P pool.
  • k: The rate of P release.

This approach measures P as a dynamic process.

Measuring Success: The Key Outcomes

We tested the models against three agronomic metrics:

1. Normalized Yield (\(Y_{norm}\)) - How well did the crop perform relative to its maximum potential at that specific site?

2. P-Export (\(P_{up}\)) - How much phosphorus did the crop remove from the field?

3. P-Balance (\(P_{bal}\)) - What is the long-term surplus or deficit of P in the soil? This is a key indicator of sustainability.

How We Compared the Models

To ensure a fair and robust comparison, we used a consistent statistical approach:

1. Linear Mixed-Effects Models (lmer) - We built a separate model for each agronomic outcome (Yield, P-Export, P-Balance). - This approach accounts for the nested structure of the STYCS experiment (sites, years, blocks).

2. Standardized Coefficients (β) - All numeric variables were scaled and centered (mean=0, sd=1). - This allows us to directly compare the effect size of each predictor. A larger coefficient means a stronger effect.

3. The Comparison - In the following tables, each column represents a separate model where we test a different set of predictors.

What Do the P Metrics Actually Measure?

A robust P metric should reflect both the soil’s inherent properties (like texture and pH) and the impact of management (fertilization). We modeled each metric to see what drives it.

Model PS k J0 P-CO2 P-AAE10
Alox 0.136 -0.660 -1.204 -0.034 -0.319
Feox -0.098 0.020 -0.571 -0.164 -0.138
Clay -0.062 -1.733** 0.611 -0.007 -0.121
C-org 0.351* 1.044** -0.412 0.166 0.232
pH -0.058 -0.280 0.094 0.075 0.057
Silt -0.046 0.252 0.113 -0.084 0.012
marginal R² 0.175 0.204 0.224 0.125 0.280
conditional R² 0.894 0.963 0.976 0.724 0.832

Predicting Yield: The Standard Test Excels

First, we tested which P metric was best at predicting site-normalized yield (\(Y_{norm}\)).

Model P-CO2 only P-AAE10 only GRUD Model Kinetic Model
k 0.166
J0 -0.012
PS 0.066
P-AAE10 0.067* 0.432**
P-CO2 0.027 -0.128
P-CO2 * P-AAE10 0.149*
marginal R² 0.012 0.084 0.291 0.019
conditional R² 0.083 0.361 0.436 0.045

Predicting P-Export: A mixed Picture

Model P-CO2 only P-AAE10 only GRUD Model Kinetic Model
k -0.014
J0 0.080
PS -0.018
P-AAE10 0.025 -0.015
P-CO2 0.087 0.131
P-CO2 * P-AAE10 0.011
marginal R² 0.012 0.001 0.016 0.004
conditional R² 0.654 0.685 0.796 0.789

Observation: Here, the results are less clear. P-Export is a more complex variable to predict, and no single model or predictor stands out as being consistently powerful. ## P-balance model summary:

Predicting P-Balance: The Kinetic Model is Superior

Model P-CO2 only P-AAE10 only GRUD Model Kinetic Model
k 0.155
J0 -0.151
PS 0.341***
P-AAE10 0.009 0.009
P-CO2 -0.023 -0.029
P-CO2 * P-AAE10 0.030
marginal R² 0.001 0.000 0.006 0.122
conditional R² 0.590 0.762 0.596 0.699

Key Findings

  1. A Robust Kinetic Model was Developed
    • The original linearized method was shown to be invalid for these soils.
    • Our non-linear approach provided a superior and statistically robust fit.
  2. Predictive Power is Purpose-Dependent
    • For predicting yield, the standard soil test (\(P_{AAE10}\)) was the most effective predictor.
  3. Kinetics Excel for Long-Term Assessment
    • For predicting the P-Balance, the kinetic parameter PS (the P pool) was vastly superior, while standard tests showed no predictive power.

The Right Tool for the Right Job

My research concludes that the ideal soil P test depends on the question being asked:

For Routine Fertilization

To answer a farmer’s question: “Is P limiting my yield this year?”

The Standard Soil Tests are effective and well-suited.

For Long-Term Sustainability

To answer a policymaker’s question: “Is this soil’s P status sustainable?”

A Kinetic Approach is the superior and necessary tool.